Three-dimensional modeling applications generate, manipulate, or otherwise use computer-generated models of three-dimensional objects. Simulating a three-dimensional object in a realistic manner may be difficult due to the complexities of how light interacts with real-world materials. For example, real-word objects may exhibit sub-surface scattering effects in which light enters one point of a surface, is diffusively reflected through the surface, and exits at another point in the surface. Variations in the sub-surface scattering of light through translucent materials such as ceramics, plastics, rubbers and flesh may cause portions of the material to appear more or less saturated in color.
For example, FIG. 1 depicts an example of an object 102 illuminated by light that has undergone sub-surface scattering. The object 102 includes a uniformly illuminated surface 104 and an occluded surface 106 at a right angle to the uniformly illuminated surface 104. The occluded surface 106 includes a region 108 that appears black or nearly black in color and a region 110 that appears to have a more saturated version of the color of the illuminated surface 104.
FIG. 2 is a lateral view of the object 102 that depicts the sub-surface scattering of light 204 through the object 102. A light source 202 emanates light toward the surface 104. The light 204 enters the object 102 via the surface 104. Some of the light 204 is fully absorbed by the object 102. The absorption of the light 204 prevents light from exiting the surface 106 in the region 108, thereby causing the region 108 to appear black or nearly black in color. Some of the light 204 is scattered and exits the object 102 through the surface 104. Some of the light 204 travels through the object 102 and exits the object 102 at the region 110. The light 204 that exits at the region 110 may travel further through the object 102 than light that enters and exits the object 102 via the surface 104. The light 204 that exits at the region 110 may therefore experience greater sub-surface scattering than light that enters and exits the surface 104. The greater sub-surface scattering of the light 204 exiting at the region 110 may cause coloring of the region 108 to appear more saturated to the human eye than the light exiting via the surface 104.
Simulating the sub-surface scattering effects depicted in FIGS. 1-2 in a realistic manner may involve extensive processing resources. To avoid excessive use of processing resources, prior solutions for simulating three-dimensional objects omitted the simulation of sub-surface scattering or used overly simplistic computational models that reduced the realism with which the sub-surface scattering effects were rendered.
Improved methods for simulating sub-surface scattering in the illumination of simulated three-dimensional objects are desirable.